Fluctuation-Dissipation Theorems and Entropy Production in Relaxational Systems

We show that for stochastic dynamical systems out of equilibrium the violation of the fluctuation-dissipation equality is bounded by a function of the entropy production. The result applies to a much wider situation than “near equilibrium,” comprising diffusion as well as glasses and other macroscopic systems far from equilibrium. For aging systems this bounds the age-frequency regimes in which the susceptibilities satisfy the fluctuation-dissipation theorem in terms of the rate of decay of the $H$ function, a question intimately related to the reading of a thermometer placed in contact with the system.